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Mathematics

Solution of equations x + y = 8 and 3x - 5y = 0 is :

  1. x = 5, y = -3

  2. x = 5, y = 3

  3. x = -5, y = 3

  4. x = -5, y = -3

Linear Equations

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Answer

Given, equations :

⇒ x + y = 8 and 3x - 5y = 0

⇒ x + y - 8 = 0 ………..(1)

⇒ 3x - 5y = 0 ……….(2)

By cross-multiplication method :

⇒x1×0−(−5)×(−8)=y(−8)×3−0×1=11×(−5)−3×1⇒x0−40=y−24−0=1−5−3⇒x−40=y−24=1−8⇒x−40=1−8 and y−24=1−8⇒x=−40−8 and y=−24−8⇒x=5 and y=3.\Rightarrow \dfrac{x}{1 \times 0 - (-5) \times (-8)} = \dfrac{y}{(-8) \times 3 - 0 \times 1} = \dfrac{1}{1 \times (-5) - 3 \times 1} \\[1em] \Rightarrow \dfrac{x}{0 - 40} = \dfrac{y}{-24 - 0} = \dfrac{1}{-5 - 3} \\[1em] \Rightarrow \dfrac{x}{-40} = \dfrac{y}{-24} = \dfrac{1}{-8} \\[1em] \Rightarrow \dfrac{x}{-40} = \dfrac{1}{-8} \text{ and } \dfrac{y}{-24} = \dfrac{1}{-8} \\[1em] \Rightarrow x = \dfrac{-40}{-8} \text{ and } y = \dfrac{-24}{-8} \\[1em] \Rightarrow x = 5 \text{ and } y = 3.

Hence, Option 2 is the correct option.

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